COVARIANT OPERATOR FORMALISM OF TWO-DIMENSIONAL TOPOLOGICAL GRAVITY

1992 ◽  
Vol 07 (13) ◽  
pp. 3105-3131
Author(s):  
NORIAKI IKEDA
Keyword(s):  
Quantum Gravity ◽  
Two Dimensional ◽  
Operator Formalism ◽  
Canonical Operator ◽  
Covariant Operator ◽  
Gauge Fixing ◽  
Topological Gravity

The manifestly covariant canonical operator formalism of two-dimensional topological gravity is formulated. Its unitarity is confirmed by means of constructing the Kugo–Ojima's quartets. A number of new symmetries are found by adopting a particular gauge fixing condition. These symmetries correspond to the "choral symmetry" generated by the 4N-dimensional Poincaré-like superalgebra in the ordinary N-dimensional quantum gravity.

COVARIANT OPERATOR FORMALISM OF TWO-DIMENSIONAL TOPOLOGICAL GRAVITY II

1992 ◽  
Vol 07 (02) ◽  
pp. 131-145
Author(s):  
NORIAKI IKEDA
Keyword(s):  
Lagrangian Density ◽  
Two Dimensional ◽  
Operator Formalism ◽  
Canonical Operator ◽  
Covariant Operator ◽  
Gauge Fixing ◽  
Topological Gravity

Zweibein formalism of two-dimensional topological gravity is formulated in the framework of the manifestly covariant canonical operator formalism. By adopting the new gauge fixing condition, we extend the symmetries of the Lagrangian density, generated by the modified Poincaré-like superalgebra. The intrinsic topological BRS transformation introduced by the previous paper is still the symmetry of the theory.

UNITARY THEORY OF TWO-DIMENSIONAL QUANTUM GRAVITY AND ITS EXACT COVARIANT OPERATOR SOLUTION

1991 ◽  
Vol 06 (22) ◽  
pp. 3955-3971 ◽  
Author(s):  
MITSUO ABE ◽  
NOBORU NAKANISHI
Keyword(s):  
Quantum Gravity ◽  
Two Dimensional ◽  
Operator Formalism ◽  
Unitary Theory ◽  
Operator Solution ◽  
Canonical Operator ◽  
Weyl Invariance ◽  
Covariant Operator ◽  
Gauge Fixing

The manifestly covariant canonical operator formalism of two-dimensional quantum gravity is formulated on the basis of Sato’s gauge-fixing of the Weyl invariance. The unitarity problem, due to ghost-counting mismatch, is resolved by making the gravitational FP ghosts also play the role of the Weyl FP ghosts. All two-dimensional (anti)commutators between fundamental fields are explicitly obtained.

scholarly journals HUGE SPACE-DEPENDENT SYMMETRY IN THE LIGHTCONE GAUGE TWO-DIMENSIONAL QUANTUM GRAVITY

1996 ◽  
Vol 11 (15) ◽  
pp. 2623-2642 ◽  
Author(s):  
MITSUO ABE ◽  
NOBORU NAKANISHI
Keyword(s):  
Quantum Gravity ◽  
Current Algebra ◽  
Symmetry Algebra ◽  
Local Version ◽  
Two Dimensional ◽  
Operator Formalism ◽  
Canonical Operator ◽  
Coordinate Invariance

The lightcone gauge two-dimensional quantum gravity, i.e. the local version of Polyakov’s “induced” quantum gravity, is analyzed in the canonical operator formalism. An extremely huge x+-dependent symmetry algebra is found to exist in this model. Both Polyakov’s SL (2, R) current algebra and residual general coordinate invariance are very very tiny subalgebras of it.

PERTURBATIVE RECONFIRMATION OF THE EXACT COVARIANT SOLUTION TO THE TWO-DIMENSIONAL QUANTUM GRAVITY

1992 ◽  
Vol 07 (25) ◽  
pp. 6405-6420 ◽  
Author(s):  
MITSUO ABE ◽  
NOBORU NAKANISHI
Keyword(s):  
Exact Solution ◽  
Perturbation Theory ◽  
Quantum Gravity ◽  
Finite Number ◽  
Two Dimensional ◽  
Operator Formalism ◽  
Perturbative Approach ◽  
Covariant Operator ◽  
Feynman Graphs ◽  
Field Redefinition

The validity of the exact solution to the covariant operator formalism of two-dimensional quantum gravity is reconfirmed by means of the conventional perturbation theory. Only a finite number of Feynman graphs are encountered, yet, the perturbative approach is much more complicated than the exact method. A unitarized, covariantized Polyakov theory, which has an infinite number of Feynman graphs, is obtained from the above result by a simple field redefinition.

A Continuum Approach to 2D-Quantum Gravity for c>1

1997 ◽  
Vol 11 (26n27) ◽  
pp. 3247-3279
Author(s):  
M. Martellini ◽  
M. Spreafico ◽  
K. Yoshida
Keyword(s):  
Quantum Gravity ◽  
Scalar Curvature ◽  
Free Parameter ◽  
Central Charge ◽  
Flat Space ◽  
String Tension ◽  
Physical Significance ◽  
Two Dimensional ◽  
Continuum Approach ◽  
Gauge Fixing

Two dimensional induced quantum gravity with matter central charge c>1 is studied by carefully treating both diffeomorphism and Weyl symmetries. It is shown that, for the gauge fixing condition R(g) (scalar curvature) = const, one obtains a modification of the David–Distler–Kawai version of KPZ scaling. We obtain a class of models with real string tension for all values c>1. They contain a free parameter which is, however, strongly constrained by the requirement of the non triviality of the model. The possible physical significance of the new model is discussed. In particular we note that it describes smooth surfaces imbedded in d-dimensional flat space time for arbitrary d, which is consistent with recent numerical results for d=3.

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